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(I) If ( a 3 + 1 , B − 2 3 ) = ( 5 3 , 1 3 ) Find the Values of a and B. - Mathematics

(i) If \[\left( \frac{a}{3} + 1, b - \frac{2}{3} \right) = \left( \frac{5}{3}, \frac{1}{3} \right)\] find the values of a and b

 

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Solution

(i)  \[\left( \frac{a}{3} + 1, b - \frac{2}{3} \right) = \left( \frac{5}{3}, \frac{1}{3} \right)\]

By the definition of equality of ordered pairs, we have:

\[\left( \frac{a}{3} + 1, b - \frac{2}{3} \right) = \left( \frac{5}{3}, \frac{1}{3} \right)\]

\[\Rightarrow \left( \frac{a}{3} + 1 \right) = \frac{5}{3} \text{ and } \left( b - \frac{2}{3} \right) = \frac{1}{3}\]
\[ \Rightarrow \frac{a}{3} = \frac{5}{3} - 1 \text{ and } b = \frac{1}{3} + \frac{2}{3}\]
\[ \Rightarrow \frac{a}{3} = \frac{2}{3} \text{ and } b = 1\]
\[ \Rightarrow a = 2\text{  and  } b = 1\]

Concept: Sets - Equality of Ordered Pairs
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 2 Relations
Exercise 2.1 | Q 1.1 | Page 8
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